Answer to Question #192112 in Statistics and Probability for sagun poudel

Question

Weight of students of a class having 40 student was recorded. This data is given in the following table. Perform the tasks given in (i) to (iv) on the data given below using a spreadsheet package: (6 Marks)

(Weight in Kgs)

42 54 60 55 49 46 55 38 65 40

61 46 47 42 51 53 59 57 46 60

52 54 50 60 58 44 49 39 48 56

47 53 52 57 55 44 51 47 61 43

(i) Find the minimum and maximum weight using the spreadsheet formula.

(ii) Create 6 classes with suitable class intervals and create the frequency distribution.

You must use Array formula.

(iii) Find the percentage of the students whose weight is less than the mean weight

(iv) Draw the histogram for the data above. Also try to relate it to normal distribution

curve.

Answer 1

(i) Maximum weight =max( 42, 54, 60, 55, 49, 46, 55, 38, 65, 40, 61, 46, 47, 42, 51, 53, 59, 57, 46, 60,52, 54, 50, 60, 58, 44, 49, 39, 48, 56,47, 53, 52, 57, 55, 44, 51, 47, 61, 43)=38 kg

Minimum weight =min( 42, 54, 60, 55, 49, 46, 55, 38, 65, 40, 61, 46, 47, 42, 51, 53, 59, 57, 46, 60,52, 54, 50, 60, 58, 44, 49, 39, 48, 56,47, 53, 52, 57, 55, 44, 51, 47, 61, 43)=65 kg

(ii) Class interval and frequency distribution shown in the table below-

Mean weight $\bar{x}=\dfrac{\sum (weights)}{40}=\dfrac{2046}{40}=51.15 kg$

(iii)Number of students whose weight is less than the mean weight = 18

Percentage is$=\dfrac{18}{40}\times 100=45$ %

(iv) Histogram for the above distribution is-

The following data can be relates to normal distribution with mean weights of 51.15 kg and assume that the sample size of the weights also above 30. So given data can be represented in Normal distribution.