The table below shows the scores on a math test. David 75 Aaron 75 Ashley 60 Gina 75 Andrew 75 Kei 95 Monica 100 Anna 60 Lucas 75 Jennifer 65 The number of standard deviations between a score and the mean score is indicated by a z-score. What was Ashley's z-score on the math test?
a. 1.1
c. -1.1
b. 60
d. -15.5
Answers
Answer: c
Step-by-step explanation: good luck everyone
Ashley's z-score for the given table is -1.2.
What is z-score?''A z-score describes the position of a raw score in terms of its distance from the mean, when measured in standard deviation units. The z-score is positive if the value lies above the mean, and negative if it lies below the mean.''
From the given table, we can calculate the mean, median, mode and standard deviation.
Therefore, mean = (75 + 60 + 75 + 100 + 75 + 75 + 75 + 95 + 60 + 65) ÷ 10
= 75.5
Median = middle term when scores are arranged in ascending order
= middle term of {60, 60, 65, 75, 75, 75, 75, 75, 95, 100}
= 75
Mode = number that occurs highest in {60, 60, 65, 75, 75, 75, 75, 75, 95, 100} = 75.
Standard deviation = [tex][\sqrt{(x_1-x)^{2}+(x_2-x)^{2}+........+(x_n-x)^{2}]/n[/tex]
= [tex][\sqrt{(75-75.5)^{2}+(60-75.5)^{2}+........+(65-75.5)^{2}]/10[/tex]
= [tex]\sqrt{157.25}[/tex]
=12.54
Therefore, Ashley's Z-score = (Ashley's score - Mean)/ Standard Deviation
= (60 - 75.5)/12.54 = -1.2
Learn more about z-score here: https://brainly.com/question/17756962
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