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The table shows the number of Calories in twelve different snacks. Which measure of central tendency would be most affected by the outlier 342 Calories?

Number of Calories in Snacks

122

87

149

121

64

138

342

72

179

105

99

114

Fmean H mode

Gmedian J range

Short Answer

Expert verified

The option Fis correct.

Step by step solution

01

Step 1. State the concept. 

Mean absolute deviation is given by the formula:

|x¯x1|+|x¯x2|++|x¯xn|n, where x¯is the mean and xiare the terms.

02

Step 2. Calculate the mean. 

First calculate the mean number of calories in the snacks.

x¯=122+64+179+87+138+105+149+342+99+121+72+11412=159212=132.667133

03

Step 3. Calculate the mean absolute deviation.

In order to find mean absolute deviation, first find the absolute values of the differences.

|x¯x1|=|133122|=11|x¯x2|=|13364|=69|x¯x3|=|133179|=46|x¯x4|=|13387|=46|x¯x5|=|133138|=5|x¯x6|=|133105|=28|x¯x7|=|133149|=16|x¯x8|=|133342|=209|x¯x9|=|13399|=34|x¯x10|=|133121|=12|x¯x11|=|13372|=61|x¯x12|=|133114|=19

Now calculate mean absolute deviation.

11+69+46+46+5+28+16+209+34+12+61+1912=46.33

Hence, mean will be that measure of central tendency that would be most affected by the outlier 342 Calories. Therefore, option Fis correct.

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