Question

Two standardized​ tests, A and​ B, use very different scales of scores. The formula Upper A = 20* B + 200 approximates the relationship between scores on the two tests. Use the summary statistics for a sample of students who took test B to determine the summary statistics for equivalent scores on test A.

Lowest score equals 21 Mean equals 25 Standard deviation equals 3 Q3 equals 28 Median equals 26 IQR equals 5 Find the summary statistics for equivalent scores on test A.

Find the summary statistics for equivalent scores on test A.

a. Lowest score =

b. Mean=

c. Standard deviation=

d. Q3 =

e.Median =

f. IQR

Answer 1

We know that values like minimum, maximum, median, mean, Q1 and Q3 are dependent on each data value whereas values like IQR and standard deviation depends only on the differences between data values.

Therefore, standard deviation and IQR will only be multiplied by 20 and minimum, maximum, median, mean, Q1 and Q3 will be calculated using the given formula

A = 20* B + 200

Data values for B are given as

(A)Lowest score of B = 21

this implies, lowest score for A = 20*21 + 200 = 620

(B) mean score of B = 25

this implies, mean score for A = 20*25 + 200 = 700

(C) standard deviation of B = 3

this implies, standard deviation for A = 20*3 = 60

(D) Q3 for B = 28

this implies, Q3 for A = 20*28 + 200 = 760

(E) Median for B = 26

this implies, median for A = 20*26 + 200 = 720

(F) IQR for B = 5

this implies, IQR for A = 20*5 = 100