Statistical Analysis of Mean, Mode, Median & Data Distribution

This assignment focuses on statistical analysis, specifically calculating and interpreting the mean, mode, median, and data distribution. It includes tasks where the mean is calculated for different experimental conditions, such as a cat food study and a telesales positive reinforcement scheme. The assignment further explores the mode by identifying the most frequent score in various datasets. The median is determined by arranging data in ascending order and finding the middle value. Additionally, the assignment covers the concept of range, calculated for different groups of data. Finally, it delves into frequency graphs, analyzing and interpreting data distribution across different value ranges, and associating frequency graphs with provided data groups. Desklib provides students access to this solved assignment and many more resources to aid in their studies.

Online Activity 13.1: The mean, the mode and the median
Task 1: The mean
Mean is calculated by first adding all the individual values together. This total is then divided by
the number of values.
Study 1
A group of psychologists conducted a small pilot study to test evaluative conditioning with a
new brand of cat food. They recruited ten cat owners to an experiment with a between-
participants design (participants take part in only one condition). Five were randomly assigned
to the experimental condition where they saw an image of the new food immediately after
seeing an image of a cute kitten. The slide show also contained other, neutral images. The other
five cat owners were assigned to the control condition, where they saw the same images, but the
image of the new food was not paired with that of a young kitten. All ten participants were then
asked to rate how favourable they found the new cat food on a scale of 0 to 100. A higher score
represented a more favourable attitude. The scores for the participants are presented below.
Scores from participants in the experimental
condition
Scores from participants in the control
condition
74 28
56 75
62 49
31 59
57 39
Using the calculator tool, calculate the mean score for each condition and enter it into the space
below.
The total = 74 + 56 + 62 + 31 + 57 = 280
Mean = Total/No. of Observations = 280/5 = 56
Then divide the total by ‘5’ (as there are 5 individual values)

Mean scores for participants in the experimental condition
56
Mean score for participants in the control condition
Total = 28+75+49+59+39 = 250
Mean = Total/No. of observation = 250/5 = 50
50
Task 1: The mean (cont.)
Study 2
A researcher was asked by a telesales company to test the effectiveness of a positive
reinforcement scheme based on giving ‘gold stars’ to employees who performed well. The
researcher recruited twelve employees and randomly assigned six to the gold-star condition
(these six received a gold star if they exceeded their daily sales quota) and six to a control
condition that did not receive gold stars. The researcher recorded the total number of sales made
by each participant in a two-week period. The scores from this experiment are presented in the
table below.
Sales made by the participants in the gold-
star condition
Sales made by the participants in the
control condition
53 95
84 78
76 47
51 79
89 68
79 77
Using the calculator tool, calculate the mean score for each condition and enter it into the space
below.
Sales made by the participants in the gold-star condition

Total = 53+84+76+51+89+79 = 432
Mean = Total/No. of observation = 432/6 = 72
72
Sales made by the participants in the control condition
Total = 95+78+47+79+68+77=444
Mean = Total/No. of observation = 444/6 = 74
74
Task 2: The mode
Mode is – the most common score.
Now work out the mode for each of the following three sets of scores.
Data set 1
10
0
85 60 70 90 85 70 85 60 85
Which is the mode?
Arranging in ascending order
60, 60, 70, 70, 85, 85, 85, 85, 90, 100
70
85 would be the mode of this data set
60
Data set 2

22 1 12 15 16 1 18 15 1 19
Which is the mode?
Arranging in ascending order
1, 1, 1, 12, 15, 15, 16, 18, 19, 22
1 would be the mode of this data set
15
12
Data set 3
1
2
12 12 8 5 15 9 8 1
1
8
Which is the mode?
Arranging in ascending order
5, 8, 8, 8, 9, 11, 12, 12, 12, 15
12
8
8 and 12 would be the modes of this data set
Task 3: The median
The median is the score that is in the middle of a set of scores that have been put in order of
magnitude.
Now work out the median for the following three sets of scores. Remember to put each set
in order of magnitude first.

Data set 1
10
0
85 60 70 90 85 70 85 60 85
Which is the median?
Arranging in ascending order
60, 60, 70, 70, 85, 85, 85, 85, 90, 100
Middle two numbers = (85, 85)
Median = (85+85)/2 = 85
70
85 median number
60
Data set 2
22 1 12 15 16 1 18 15 1 19
Which is the median?
Arranging ascending order
1, 1, 1, 12, 15, 15, 16, 18, 19, 22
Middle two numbers (15, 15)
Median = (15+15)/2 = 15
1

15 median number
16
Data set 3
1
2
12 12 8 5 15 9 8 1
1
8
Which is the median?
Arranging in ascending order
5, 8, 8, 8, 9, 11, 12, 12, 12, 15
Middle two numbers = (9, 11)
Median = (9+11)/2 = 10
11
9
10 median number

Online Activity 13.2: Distribution
Task 1: Calculating the range
Group
1:
46 52 53 48 5
1
48 51 52 49 50
Group
2:
64 35 19 43 1
2
56 82 25 91 73
Group
3:
89 91 13 16 8
5
14 15 12 81 84
Group 1
46 52 53 48 51 48 51 52 49 50
Arranging in ascending order
46, 48, 48, 49, 50, 51, 51, 52, 52, 53
Highest number = 53
Lowest number = 46
Range = 53 – 46 = 7
7
Group 2
64 35 19 43 12 56 82 25 91 73
Arranging in ascending order
12, 19, 25, 35, 43, 56, 64, 73, 82, 91
Highest number = 91

Lowest number = 12
Range = 91 – 12 = 79
79
Group 3
89 91 13 16 85 14 15 12 81 84
Arranging in ascending order
12, 13, 14, 15, 16, 81, 84, 85, 89, 91
Highest number = 91
Lowest number = 12
Range = 91 – 12 = 79
79
Frequency graphs
The figure above shows a frequency bar graph. The axis on the horizontal that has four
points is labelled ‘value’ the 4 points are; 0-24, 25-49, 50-74 and 75-100. The axis on the
vertical is labelled ‘frequency’ and has a scale from 0 to 10, 0 is the point of origin where

the x and y axes would intersect and the maximum y-axis point is equivalent to 10 on the
graph. The graph has a single bar and its x-axis value ranges from 0-24 and its y-axis value
is ‘2’. This is an indication that we have two scores within the set of value between 0 and 24.
To complete the graph, we now need to work out how many values are ‘between 25 and 49’,
‘between 50 and 74’ and ‘between 75 and 100’.
12, 19, 25, 35, 43, 56, 64, 73, 82, 91
0 – 24 = 2
25 – 49 = 3
50 – 74 = 3
75 – 100 = 2
0-24 25-49 50-74 75-100
0
0.5
1
1.5
2
2.5
3
The graph above shows a frequency of 4 scores categories. The axis on the horizontal that
has four points is labelled ‘value’ the 4 points are; 0-24, 25-49, 50-74 and 75-100. The axis
on the vertical is labelled ‘frequency’ and has a scale from 0 to 10, 0 is the point of origin
where the x and y axes would intersect and the maximum y-axis point is equivalent to 10 on
the graph. The first bar x-axis value ranges from 0-24 and its y-axis value is ‘2’. The
second bar x-axis value ranges from 25-49 and its y-axis value is ‘3’. The third bar x-axis
value ranges from 50-74 and its y-axis value is ‘3’. The fourth bar x-axis value ranges from
75-100 and its y-axis value is ‘2’.
Task 2: Distribution of data from the learner drivers experiment

Group
1
46 52 53 48 5
1
48 51 52 49 50
Group
2
64 35 19 43 1
2
56 82 25 91 73
Group
3
89 91 13 16 8
5
14 15 12 81 84
Graph A
The data of which group is displayed in Graph A?
Group 1 46 52 53 48 51 48 51 52 49 50
Arrange in ascending order
46, 48, 48, 49, 50, 51, 51, 52, 52, 53
0 – 24 = 0
25 – 49 = 4
50 – 74 = 6
75 – 100 = 0
Group 2 64 35 19 43 12 56 82 25 91 73
12, 19, 25, 35, 43, 56, 64, 73, 82, 91
0 – 24 = 2

25 – 49 = 3
50 – 74 = 3
75 – 100 = 2
Group 3 89 91 13 16 85 14 15 12 81 84
12, 13, 14, 15, 16, 81, 84, 85, 89, 91
0 – 24 = 5
25 – 49 = 0
50 – 74 = 0
75 – 100 = 5
Group 1
Group 2
The graph above shows a frequency of 4 scores categories. The axis on the horizontal that
has four points is labelled ‘value’ the 4 points are; 0-24, 25-49, 50-74 and 75-100. The axis
on the vertical is labelled ‘frequency’ and has a scale from 0 to 10, 0 is the point of origin
where the x and y axes would intersect and the maximum y-axis point is equivalent to 10 on
the graph. The first bar x-axis value ranges from 0-24 and its y-axis value is ‘2’. The
second bar x-axis value ranges from 25-49 and its y-axis value is ‘3’. The third bar x-axis
value ranges from 50-74 and its y-axis value is ‘3’. The fourth bar x-axis value ranges from
75-100 and its y-axis value is ‘2’.
This shows that 2 values were between 0 and 24, 3 values were between 25 and 49, 3 scores
Between 50 and 74 and 2 score between 75 and 100
Group 3
Graph B

The data of which group is displayed in Graph B?
Group 1 46 52 53 48 51 48 51 52 49 50
Arrange in ascending order
46, 48, 48, 49, 50, 51, 51, 52, 52, 53
0 – 24 = 0
25 – 49 = 4
50 – 74 = 6
75 – 100 = 0
Group 1
The graph above shows a frequency of 2 scores categories. The axis on the horizontal that
has four points is labelled ‘value’ the 4 points are; 0-24, 25-49, 50-74 and 75-100. The axis
on the vertical is labelled ‘frequency’ and has a scale from 0 to 10, 0 is the point of origin
where the x and y axes would intersect and the maximum y-axis point is equivalent to 10 on
the graph. The first bar x-axis value ranges from 25-49 and its y-axis value is ‘4’. The
second bar x-axis value ranges from 50-74 and its y-axis value is ‘6’.
Group 2
Group 3