If first quartile (Q1) = 30 and third quartile (Q3) = 40, which of the following must be true? I. The variance is at most 100. II. The median is 35. III. The mean is between 30 and 40

Question

If first quartile (Q1) = 30 and third quartile (Q3) = 40, which of the following must be true?

I. The variance is at most 100.

II. The median is 35.

III. The mean is between 30 and 40

How to find the mean, median and variance

Answer 1

II the median is 35 True It's the middle score.

the mean might be between 30 and 40, but that depends on whether the scores are skewed. if there

were 10 scores, 1,2,3,4,5,6,7,8, 9, and 55, the median score is 5 but the mean is 10 which is not between the 2nd and 3rd quartile. The median is the middle number. Median, quartiles and percentiles just rank them in order, without regard to skewness or variance.

if the variance = 100, the standard deviation =sqr100 = 10

using the empirical rule 68% of the scores are within 1 standard deviation from the mean, if the scores are normally distributed. They may not be. If the standard deviation >10, then the variance >100.

the median is the middle score. If the scores are an even number, then the median is the average of the 2 middle scores.

the mean is the arithmetic average of all the scores. Sum the scores, then divide by the number of scores.

Variance is the sum of squared deviations from the mean, divided by n-1 where n= the number of scores

That's the sample variance.

but if scores are not a sample, but the entire population, then divide by n.

take each score, subtract the mean, square that difference. Sum the squared differences, then divide by n-1 if it's a sample, or divide by n if it's the entire population.