Question

Q1. A sample of n = 8 scores has a mean of M = 7. One score in the sample is changed from X = 20 to X = 4. What is the value for the new sample mean?

Q2.

A sample yielded the following scores:

2, 3, 4, 4, 5, 5, 5, 6, 6, 7

Assume that the scores are measurements of a discrete variable and find the median.

Median =

Assume that the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution. (Use two decimal places.)

Mean =

Q3: A population of N = 7 scores has a mean of µ = 9. After one score is removed from the population, the new mean is found to be µ = 10. What is the value of the score that was removed? (Hint: Compare the values for ∑X before and after the score was removed.)

Please show all work

Answer 1

Q1. The sample mean is calculated as

$M=\frac{X1+X2+...+X8}{8}=7$

if one sample is 4 then

$M=\frac{4+X2+...+X8}{8}=7\Rightarrow X2+X3+...+X8=56-4=52$

Now,

If we replace 4 with 20 then,

$M=\frac{20+X2+...+X8}{8}$

$\because X2+...+X8=52$

$\therefore New, M=\frac{20+52}{8}=9$

Q2. The Sample

2, 3, 4, 4, 5, 5, 5, 6, 6, 7

Hence Median=(5+5)/2=5

and Mean

$M=\frac{2+3+....+7}{10}=4.7$

Q3. If previous mean=9 and N=7 then

$\sum X=63$

New Mean=10 and N=6 hence

$\sum X =60$

Now Difference is 63-60=3

Hemce 3 was the numeral that was removed.