Statistics Assignment: Numeracy, Data, and IT Analysis

This document presents a comprehensive solution to a statistics assignment, addressing various aspects of data analysis, numeracy, and IT applications. The assignment covers a range of topics, including basic arithmetic, percentage calculations, fraction and percentage conversions, and binary arithmetic. It also includes spreadsheet analysis, involving sorting data, using formulas, and creating graphs. The solution further explores descriptive statistics like mean, mode, median, and standard deviation, along with an analysis of spending habits based on the provided data. Scatter diagrams are used to explore relationships between marital status and spending on different items. Finally, the assignment concludes with a probability calculation. The document provides detailed explanations and step-by-step solutions to each question, making it a valuable resource for students studying statistics and data analysis. This assignment is contributed by a student to be published on the website Desklib.

Statistics
Student Name:
Instructor Name:
Course Number:
17th August 2019

Question 1
What is the result of the following calculation? Leave your answer in a tally format.
I I I I I I I - I I I I
Answer
I I I
Question 2:
What percentage of 70 does 49 equate to?
Answer
49
70∗100 %=70 %
Question 3:
a) Complete the table to show equivalent fractions and percentages.
Fraction Percentage
45
100 = 9
20
45%
2/3 2
3∗100 %=66.7 %
225
1000 = 9
40
22.5%
7/5 7
5∗100 %=140 %
b) A carton contains 150 cereal bars. What fraction of this number will each person get
when distributed to a class of 20 students?
Answer
150
20 =15
2
Question 4:
Samuel paid cash for 3 discount-priced football tickets. He was given £4.20 change from the
three £50 notes he tendered. What was the price of each ticket? Show your working.
Answer
3 P=50∗3 – 4.20

3 P=150 – 4.20
P= 150 – 4.20
3 =145.8
3 =48.6
Question 5:
a) Solve this binary arithmetic: 10011 +10101
Answer
10011 +10101 = 101000
b) Write the number 0.0101 as a power of 10.
Answer
0.0101=1.01 ×10−2
Question 6
As a promotional offer, a new hair salon offered its services at 20% discount for the first 2
weeks. Janice and her friends took advantage of the bargain and had their hair done for a total
amount of £100. Show your working.
a) What were the total savings made?
Answer
Let
C=cost before discount
100=(1−0.2)∗C
100=0.8C
C=125
125-100 = 25
£25 is the savings
b) Work out the average savings amount if 4 hairdos were done?
Answer
25
4 =6.25
£6.25 is the average savings
Question 7
Here are seven numbers. 5 12 12 8 4 10 5
a) Work out the mean of the seven numbers.
Answer
Mean=5+12+12+ 8+4 +10+5
7 = 56
7 =8
b) What is the mode of the seven numbers?
Answer

We arrange the numbers in ascending order as follows;
4 5 5 8 10 12 12
The mode is the most frequent number and in this case we have it as 5 and 12
Question 8
80 men and 120 women were asked if they enjoyed watching football.
Altogether 3 / 5 of the people said yes.
9 / 10 of the men said yes.
What fraction of the women said yes? (Show your working)
Answer
Total number who said yes is given as;
3
5∗200=120
Number of men who said yes is given as;
9
10∗80=72
Number of women who said yes is given as;
120−72=48
Fraction of women who said yes is given as;
48
120 =2
5
Thus 2
5 of the women said yes
Question 9
The table shows information about the marks of 20 students in a test.
Mark Frequency
14 2
15 5
16 4
17 4
18 5
Total 20

Students who scored less than the mean mark have to retake the test. How many students have to
retake the test? You must show your working.
Answer
Mean= ( 14∗2 ) + ( 15∗5 ) + ( 16∗4 ) + ( 17∗4 ) +( 18∗5)
20 = 28+75+64+ 68+90
20 = 325
20 =16.25
Next, we count the number of students who scored less than the mean mark.
2+5+4=11
11 students have to retake the test
Question 10
Which fraction is bigger - 3/5 or 5/9?
Answer
3
5 =0.60
5
9 =0.56
From the above, we can see that 3
5 is bigger.

Section 2
Question 11:
a) What actions or steps will you need to take to sort the given spreadsheet in alphabetical
and ascending order of Firstname.
Answer
The following steps will be undertaken to sort the data
Step 1: Highlight the first column (column A)
Step 2: Go to sort & Filter
Step 3: Choose Sort A to Z
Step 4: Choose Expand the selection

b) Write the command(s) to list/display only those who worked less than 35 hours in the
week.
Answer
The command is given as follows;
=IF(E4<35, A4, "")
In the above command, those who worked less than 35 hours will be listed with their first
names. 12 people were established to have worked less than 35 hours.
c) How many people earn above the given Average Amount?
Answer
9 people earn above the given average amount
d) Which type of graph will be suitable for representing the Net Amounts?
Answer
The suitable graph for representing the Net amounts would be the bar graph. This is given
below;

e) In which column(s) might replication have been used?
Answer
Replication might have been used in columns D and E.
f) What formula results in the value in cell H20?
Answer
The possibly used formula is;
=SUM(H4:H18)
Question 12:
Write the functions or commands for the following:
a) Give the total number of females.
Answer
=COUNTIF(C4:C18, "F")
b) Give the total number of records with hourly rate less than £25?

Answer
=COUNTIF(D4:D18, "<25")
c) Give the total number of surnames with the letter ‘p’ in them
Answer
=COUNTIF(B4:B18, "P*")
d) Sum the Net Amount for the females who earned a Net Amount greater than or equal to
£495.
Answer
=SUMIFS(H4:H18, C4:C18, "F", H4:H18, ">=495")
e) Search the database (the whole spreadsheet) to find ‘Messi’ and the corresponding
Deductions.
Answer
=VLOOKUP(Messi, $A$3:$H$18, 7,FALSE)
Assessment Part 2
a) Totals, mean, median and standard deviation, together with a discussion of what these
descriptive statistics tell us about their spending.
Answer
Food Clothing Entertainment Charitable Giving
Mean 265.91 177.27 89.09 13.64
Standard Error 23.50 16.27 9.36 3.57
Median 255.00 165.00 100.00 15.00
Mode #N/A 230.00 100.00 0.00
Standard Deviation 77.94 53.96 31.05 11.85
Sample Variance 6074.09 2911.82 964.09 140.45
Kurtosis -0.69 -0.66 -0.89 1.34
Skewness 0.40 -0.12 0.12 0.84

Range 240.00 180.00 95.00 40.00
Minimum 160.00 80.00 45.00 0.00
Maximum 400.00 260.00 140.00 40.00
Sum 2925.00 1950.00 980.00 150.00
Count 11 11 11 11
The average amount spent on food by the respondents is £265.91 with a median amount
spent on food being £255.00. The average amount spent on clothing by the respondents is
£177.27 with a median amount spent on clothing being £165.00. The average amount
spent on entertainment by the respondents is £89.09 with a median amount spent on
entertainment being £100.00. Lastly, the average amount spent on charitable giving by
the respondents is £13.64 with a median amount spent on charitable giving being £15.00.
In overall, the above results shows that respondents spend more on food followed by
clothing then entertainment and lastly on charitable giving.
b) Graphical summaries for each of the four items
Answer

c) Scatter diagrams to explore the relationship between marital status and each of the four
spending items. Discuss.
Answer

The above plot shows that there is a positive relationship between spending on food and
marital status. Married people spend more on food as compared to the single persons.
The above plot shows that the single persons tend to spend more on clothing as compared
to the married persons.