Univariate Data Descriptors - AP Statistics

In order to find the first and third quartiles, we haave to find the 25th and 75th percentiles, respectively.

To find the percentile, we find the product of and the number of items in the set.

We then round that number up if it is not a whole number, and the term in the set is the percentile.

For this problem, to find the and percentile, we first find that there are 14 items in the set. We find their respective products to be

and

As such, the and percentiles are the fourth and eleventh terms in the set, or

The -percentile is the value such that percent of values are less than it.

Using a normal table or calculator (such as R, using the command qnorm(0.9)), we get that the approximate -percentile is about .

In order to find the first and third quartiles, we haave to find the 25th and 75th percentiles, respectively.

To find the percentile, we find the product of and the number of items in the set.

We then round that number up if it is not a whole number, and the term in the set is the percentile.

For this problem, to find the and percentile, we first find that there are 14 items in the set. We find their respective products to be

and

As such, the and percentiles are the fourth and eleventh terms in the set, or

Standard deviation is essentially the average distance from the mean of a group of numbers. There are a number of steps in computing standard deviation, but the steps are not too complicated if you take them one at a time. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide this value by the number of values. Finally, find the square root of the result.

1:

2:

3:

4:

5:

Variation measures the average difference between values within a group. The process is not complicated but there are four steps that can take time. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide this value by the number of values in the group minus one (in this case, there are four days).

1:

2:

3:

4:

Note that to find the standard deviation, we would simply take one additional step of finding the square root of the variance.

This question illustrates the close relationship between the concepts of variance and standard deviation. We can find variance even though we do not know the values in the population if we know the standard deviation. Simply square the standard deviation to find the variance.

There are five steps to finding the standard deviation of a group of values. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide this value by the number of values minus one. Finally, find the square root of the result.

There are four steps to finding the variance of values within a group. First, find the mean of the values. Second, subtract the mean from the first value and square the result. Do this for all remaining values. Third, add these results together. Fourth, divide the result by the number of values in the group minus one (in this case, there are seven days, so you must divide by six).

To find the mean of the whole population, multiply the female's average by the number of females, and then multiply the male's average by the number of males. Sum up these products and divide by the total number of males AND females:

The range is the simplest measurement of the difference between values in a data set. To find the range, one simply subtracts the lowest value from the greatest value, ignoring the others. Here, the lowest value is 155 and the greatest is 720.

The range is the simplest measurement of the difference between values in a data set. To find the range, simply subtract the lowest value from the greatest value, ignoring the others.

The range is the simple measurement of the difference between values in a dataset.

To find the range, simply subtract the lowest value from the greatest value, ignoring the others.

To find the range, subtract the minimum value from the maximum value

minimum:

maximum:

So,

maximum - minimum =

To find the range, subtract the minimum value from the maximum value

minimum:

maximum:

So,

maximum - minimum =

The range is equal to the absolute difference between the minimum and maximum value.

We find the range to be

The Interquartile Range equation is Q3-Q1

First, make sure the data is in ascending order. Then split the data up so that it each quartile has 25% of the data, or think of it as splitting the data into 4 equal parts.

• is the "middle" value in the first half of the rank-ordered data set.
• is the median value in the overall set.
• is the "middle" value in the second half of the rank-ordered data set.

To find the interquartile range, first find the median. This will split the data set into the upper and lower halves. The median for this data set is 11.

Focusing on the lower half, we can find the median, which is the first quartile, Q1:

the median is 6

Focusing on the upper half, we can find the median, which is the third quartile, Q3:

the median is 22.

The interquartile range is just Q3 - Q1, in this case

To find the interquartile range, first find the median. This will split the data set into the upper and lower halves. The median for this data set is 15.

Focusing on the lower half, we can find the median, which is the first quartile, Q1:

the median is 6, found by taking the mean of the middle two numbers 5 and 7.

Focusing on the upper half, we can find the median, which is the third quartile, Q3:

the median is 22.5, found by taking the mean of the middle two numbers 22 and 23.

The interquartile range is just Q3 - Q1, in this case

The mean is