Statistical Problems Using Excel

Statistical Problems Using Excel

1 Spreadsheet prepared in excel file.
2.
a. Arithmetic Mean =
∑ Weights
Number of Bags =15. 19 pounds.
Median was the ( 50+1
2 )
th
=25 . 5
observation that is the average of 25th and 26th observations.
The value was calculated as 15.2 pounds.
b. The first and the third quartiles were the, ( 50+1
4 )
th
=12 .75th
and
3∗( 50+ 1
4 )
th
=38 . 25th
observations. The values were calculated in MS Excel as 15.00 and 15.40 ponds.
c. Range (0.8 pounds) was the difference between maximum (15.50 pounds) and minimum
(14.70 pounds). Interquartile range (0.4 pounds) was the difference between the third and
first quartiles. Standard deviation was calculated using the formula
σ =∑ ( xi−x
−
)
2
n for
ungrouped data. The value was obtained as 0.24 pounds from MS Excel. Variation was
the square of standard deviation and was calculated as 0.06 pounds in MS Excel (using
standard excel functions). Coefficient of variation
c . v= s
x
− ∗100 %=1. 59 %
from excel sheet.
d. The average weight of a rice bag was 15.19 pounds and median was 15.20 pounds. The
equality of mean and median indicated the normality of the data. There were no outlier
values of the weight of rice bags and hence both measures were appropriate for the data
set. The desired weight was 15.00 pounds, and the company should worry about the
average weight filled in the rice bags.
e. Standard deviation was 0.24 pounds. Hence the interval of mean ± SD was [14.95,
15.43]. As the skewness of the data was zero, signifying that the distribution of weight in
rice bags was normal, the 95% confidence interval was calculated as [15.19 ± 2*0.24] =
[14.52, 15.48]. The population at par mean weight was 15.00, which falls in the 95%
region. Hence the loss of the company, if any, was not statistically significant. The