Question

Imagine that you have entered the following distribution of scores into the program: 7, 9, 6, 3, 7, 8, 4, 10, 7, 9. The mean of this distribution of scores would be changed the most if a score of ________ was removed from the data set.

Answer 1

Answer:

3

Step-by-step explanation:

Mean refers to the average value of the set of data.

It is the central value of the set of data.

Another word for Mean is average.

Given scores:7, 9, 6, 3, 7, 8, 4, 10, 7, 9

Solution:

Sum of observations = $7+ 9+ 6+ 3+ 7+ 8+ 4+ 10+ 7+ 9=70$

Number of observations = 10

Mean = Sum of observations/Number of observations = $\frac{70}{10}=7$

If observation 3 is removed:

Sum of observations = $7+ 9+ 6+ 7+ 8+ 4+ 10+ 7+ 9=67$

Number of observations = 9

Mean =  Sum of observations/Number of observations = $\frac{67}{9}=7.44$

If observation 4 is removed:

Sum of observations = $7+ 9+ 6+ 3+ 7+ 8+ 10+ 7+ 9=66$

Number of observations = 9

Mean = $\frac{66}{9}=7.3$

If observation 6 is removed:

Sum of observations = $7+ 9+ 3+ 7+ 8+ 4+ 10+ 7+ 9=64$

Number of observations = 9

Mean = $\frac{64}{9}=7.1$

If observation 7 is removed:

Sum of observations = $9+ 6+ 3+ 8+ 4+ 10+ 9=49$

Number of observations = 7

Mean = $\frac{49}{7}=7$

If observation 8 is removed:

Sum of observations = $7+ 9+ 6+ 3+ 7+ 4+ 10+ 7+ 9=62$

Number of observations = 9

Mean = $\frac{62}{9}=6.9$

If observation 9 is removed:

Sum of observations = $7+ 6+ 3+ 7+ 8+ 4+ 10+ 7=52$

Number of observations = 8

Mean = $\frac{52}{8}=6.5$

If observation 10 is removed:

Sum of observations = $7+ 9+ 6+ 3+ 7+ 8+ 4+ 7+ 9=60$

Number of observations = 9

Mean = $\frac{60}{9}=6.7$

Therefore, mean of this distribution of scores would be changed the most if a score 3 was removed from the data set.