## a. What percent of data is greater than the 13th percentile? b. If the mean, median, and mode for a data set are all the same

a. What percent of data is greater than the 13th percentile?

b. If the mean, median, and mode for a data set are all the same, what can you conclude about the data’s distribution?

c. If the mean is greater than the mode and median for a data set, what can you conclude about the data’s distribution?

d. Mean of 3 numbers is 12. Two of them are 15 and 20. What is the third number?

e. What is the relationship between variance and standard deviation?

f. You scored in the 55th percentile on the GRE. If 8,000 people took the GRE, how many people had a score at least as high as your score?

## Answers ( )

Answer:

a) Almost 87% of the distribution is greater than the 13th percentile.

b) This indicates that the distribution is symmetrical. This doesn’t necessarily mean that the distribution is a normal distribution, but it is clear that the distribution is symmetrical.

c) This indicates that the distribution is rich skewed or positively skewed.

d) The third number that makes the mean 12 = 1.

e) The standard deviation is the square root of variance.

f) 3600 people that sat for the exam had a score at least as high as the 55th percentile’s score.

Step-by-step explanation:

a) What percent of data is greater than the 13th percentile?

The percentile serves to group a data distribution into 100 equal spaces parts. It represents the value or the point below which a particular proportion of the distribution falls.

The 13th percentile thus represent a value or a point in the distribution that is higher than 13% of the distribution.

Hence, the percentage of data greater than the 13th percentile will be just about (100-13)%, almost 87% of the distribution will be greater than the 13th percentile.

b. If the mean, median, and mode for a data set are all the same, what can you conclude about the data’s distribution?

If all the three major measures of the centre of a distribution all coincide at the same point/value, it indicates that the distribution is symmetrical. This doesn’t necessarily mean that the distribution is a normal distribution, but it is clear that the distribution is symmetrical.

c. If the mean is greater than the mode and median for a data set, what can you conclude about the data’s distribution?

The mean greater than the median and mode mean that distribution is rightly/positively skewed.

d. Mean of 3 numbers is 12. Two of them are 15 and 20. What is the third number?

The mean is the sum of variables divided by the number of variables

Mean = = (Σx)/N

x = each variable

Let the unknown third number be y

N = number of variables = 3

12 = (15 + 20 + y)/3

35 + y = 36

y = 36 – 35 = 1

e. What is the relationship between variance and standard deviation?

The variance is an average of the squared deviations from the mean.

The standard deviation is the square root of variance.

f. You scored in the 55th percentile on the GRE. If 8,000 people took the GRE, how many people had a score at least as high as your score?

Like I explained in (a), scoring 55th percentile mean that one has scored more than 55% of the people that sat for the exam.

So, the percentage of people that score as much as the 55th percentile will be the top (100-55)% of people thay sat for the exam.

45% of 8000 = 3600 people.

3600 people had a score at least as high as the 55th percentile’s score.

Hope this Helps!!!