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The table gives the distribution of heights of 100 youths at an interview

Height in cm 156-160,161-163,164-166,167-169,170-172,173-175,176-180.
Frequency 16,14,18,21,13,10,8

Using an assumed mean of 168cm calculate,correct to one decimal place :a the mean height and the standard deviation of the distribution



Answer :

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Answer:

To calculate the mean height and the standard deviation of the distribution using the assumed mean method, follow these steps:

Step 1: Calculate the assumed mean (A)

Given: Assumed mean A=168 cm

Step 2: Calculate the deviation from the assumed mean (d)

The deviation from the assumed mean for each class is calculated as:

d=Class midpoint−A

Class Midpoints:

For 156-160 cm: Midpoint =156+160/2=158

For 161-163 cm: Midpoint =161+163/2=162

For 164-166 cm: Midpoint =164+166/2=165

For 167-169 cm: Midpoint =167+169/2=168

For 170-172 cm: Midpoint =170+1722=171

For 173-175 cm: Midpoint =173+1752=174

For 176-180 cm: Midpoint =176+1802=178

Calculating d:

For each class:

156-160 cm: =158−168=−10

161-163 cm: =162−168=−6

164-166 cm: d=165−168=−3

167-169 cm: d=168−168=0

170-172 cm: d=171−168=3

173-175 cm: d=174−168=6

176-180 cm: d=178−168=10

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