Question

Two standardized​ tests, a and​ b, use very different scales of scores. the formula upper a equals 40 times upper b plus 50a=40×b+50 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= 2121 mean equals= 2929 standard deviation equals= 22 q3 equals= 2828 median equals= 2626 iqr equals= 66 find the summary statistics for equivalent scores on test
a. lowest scoreequals= nothing meanequals= nothing standard deviationequals= nothing q3equals= nothing medianequals= nothing iqrequals= nothing

Answer 1

Answer:

(a) The mean score of test A is 1210.

(b) The mean score of test A is 1210.

(c) The standard deviation of  test A is 80.

(d) The value of Q₃ for test A is 1170.

(e) The value of median for test A is 1090.

(f) The value of IQR for test A is 290.

Step-by-step explanation:

The relation between two standardized tests A and B is:

$50A=40B+50$

The equation above approximates the relationship between scores on the two tests.

The summary statistics for test B are as follows:

Lowest Score = 21

Mean score = 29

Standard deviation = 2

Q₃ = 28

Median = 26

IQR = 6

(a)

Compute the lowest score on test A as follows:

$A=40B+50\\=(40\times21)+50\\=890$

Thus, the lowest score on test A is 890.

(b)

Compute the mean score of test A as follows:

$A=40B+50\\=(40\times29)+50\\=1210$

Thus, the mean score of test A is 1210.

(c)

Compute the mean score standard deviation of test A as follows:

$A=40B+50\\=(40\times2)\\=80$

Thus, the standard deviation of  test A is 80.

(d)

Compute the value of Q₃ for test A as follows:

$A=40B+50\\=(40\times28)+50\\=1170$

Thus, the value of Q₃ for test A is 1170.

(e)

Compute the value of median for test A as follows:

$A=40B+50\\=(40\times26)+50\\=1090$

Thus, the value of median for test A is 1090.

(f)

Compute the value of IQR for test A as follows:

$A=40B+50\\=(40\times6)+50\\=290$

Thus, the value of IQR for test A is 290.