Final answer:
I have answered questions related to calculating range, variance, standard deviation, percentiles, and quartiles in various data sets.
Step-by-step explanation:
Question 1:
Range = highest value - lowest value = 19 - (-9) = 28
Variance = sum of squared deviations from the mean / number of data points = ((5-7.88)^2²+ (-7-7.88)² + ... + (10-7.88)² + (7-7.88)²) / 8 ≈ 57.75
Standard Deviation = square root of variance ≈ 7.60
Question 2:
Range = highest value - lowest value = 15 - 0 = 15
Variance = sum of squared deviations from the mean / number of data points = ((3-7)²+ (0-7)² + ... + (6-7)² + (2-7)²) / 12 ≈ 11.75
Standard Deviation = square root of variance ≈ 3.43
Question 3:
Mean = sum of all data points / number of data points = ($91 + $173 + ... + $147) / 7 = $891 / 7 ≈ $127.29
Deviation from the mean for $173 = $173 - $127.29 = $45.71
Sum of these deviations = ($45.71 + (-$56.29) + ... + $19.71) = $85.71
Range = highest value - lowest value = $173 - $57 = $116
Variance = sum of squared deviations from the mean / number of data points = (($91-$127.29)² + ($173-$127.29)² + ... + ($147-$127.29)² / 7 ≈ $6509.71
Standard Deviation = square root of variance ≈ $80.68
Question 4:
The value of the 35th percentile can't be calculated with the given data. We would need the exact data distribution to calculate it.
Question 5:
Q1 (First Quartile) = 54
Q2 (Second Quartile/Median) = 58
Q3 (Third Quartile) = 64
IQR (Interquartile Range) = Q3 - Q1 = 64 - 54 = 10
Approximate value of the 30th percentile = Q1 + (0.3 * IQR) = 54 + (0.3 * 10) = 57
Percentile rank of 61 = (Number of scores lower than 61) / Total number of scores = 7/20 * 100 = 35
Question 6:
a. Someone who scored a 500 was at the 50th percentile.
b. 20% of people scored between 650 and 700.
c. If you are at the 88th percentile, your score was approximately 750.
d. Approximately, the first quartile for SAT scores is 400 and the third quartile is 700.