1. The average income of a family of a sample of families of a village were recorded. The data is as follows

(Average monthly family income in INR)

7,235 6,230 3,500 9,000 8,000
11,500 20,000 16,000 7,250 9,000
6,000 3,000 9,000 11,000 12,500
7,250 6,750 10,000 6,750 13,500
14,000 15,000 12,000 6,050 8,000

Perform the following tasks for the data given above:

Enter the data in a spreadsheet and create a frequency distribution in the ranges: less than 5,000; 5,001 to 10,000; 10,001 to 15,000; 15,001 to 20,000; more than 20,000. Use array formula for finding the frequency distribution.

Draw the histogram of the data.

Find the mean and standard deviation of the data using spreadsheet formulae.

Find the minimum and maximum income using spreadsheet formulae.

2. A group of 8 candidates in the age group of 15 -18 years were given height enhancement exercises for a few months. The following table shows their heights before and after the exercises

Before 151 167 162 152 161 171 169 171
After 159 172 172 155 161 172 169 185

Using t-test with a significance level of can you say that the exercises helped in significant/appreciable increase in height Clearly write Ho and H1 and explain your result. Make suitable assumptions, if any.