The double dot plot shows the numbers of junk emails that were received by marcus and anders for the past twenty days. Which inference about the two populations is true?

A) Both sets of data have the same interquartile range.

B) Both sets of data have the same median

C) Ander’s data centers around 6 and Marcus’s data centers around 7

D) The Interquartile range for Ander’s data is 0. 5 greater than the interquartile range for Marcus’s data

The true inferences from the double dot plot for this case from the available options is given by: Option D) The Interquartile range for Ander’s data is 0. 5 greater than the interquartile range for Marcus’s data

What are quartiles?

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

Lower quartile, also called first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.

Similarly, second quartile (also called median) is approximately in mid of the data.

Third quartile (also called upper quartile) has approx 75% in its left partition, and on its right lies approx 25% of the data.

Left to right is said in assumption that data was arranged increasingly from left to right

How to find the interquartile range?

IQR(inter quartile range) is the difference between third and first quartile.

How does the dot plot work?

Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.

Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.

If instead of only observations, the table of unique observation and frequency is given, then we plot dots that many times as the count written in the frequency table. Thus, if its written that the value 2 has 3 has its frequency, then we plot 3 dots one over the other above the value 2 in the horizontal axis.

For this case, getting the quartiles of each dataset one by one.

For the data for Anders:

The number of dots show frequencies, therefore, from the image attached below, the data we get for Anders is:

1,2,2,3,3,5,5,5,5,5,5,6,6,6,6,7,7,7,7,7

These are total 20 observations.

Mean is the ratio of sum of all observations to the number of observations.

Sum of these values is 100, and therefore, we get:

Mean = 100/20 = 5

50% of 20 is 10 (its half). And 25% is 5, and 75% is 15.

Now, any number between the 10th and 11th value will be median because before and after that will lie ten-ten observations.

We usually take mean of these two values in such case.

The 10th value is 5, and so as the 11th value.

Thus, median of this data set is 5

Similarly, the first quartile can be taken as the average of 5th and 6th value as in mid of both lie values before which lies 25% of the data and after which lies 75% of the data.

The 5th and 6th values are 3 and 5. Their average is (3+5)/2=4

Thus, the first quartile of this data set is 4

Similarly, third quartile can be taken as average of 15th and 16th value = (6+7)/2 = 6.5

Now, the interquartile range of this dataset = third - first quartile = 6.5 - 4 = 2.5

Similarly, the data set for Marcus is:

2,3,5,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,10,10

These are total 20 observations.

Mean is the ratio of sum of all observations to the number of observations.

Sum of these values is 139, and therefore, we get:

Mean = 139/20 = 6.95 (approx 7)

Also, we get:

Median can be average of 10th and 11th value = (7+7)/2 = 7

First quartile can be average of 5th and 6th value = (6+6)/2 = 6

Third quartile can be average of 15th and 16th value = (8+8)/2 = 8

Thus, IQR = third - first quartile = 8-6 = 2

So we see that option A and B are wrong as IQR and median both are different for both the datasets.

Option C is wrong since for Ander's data, we see that both mean and median (which are central measures) evaluates to 5, so Ander's data centers around 5 instead of 6.

Option D is correct as IQR for Ander's data = 2.5 is 0.5 greater than 2 which is IQR for Marcus' data.

Thus, the true inferences from the double dot plot for this case from the available options is given by: Option D) The Interquartile range for Ander’s data is 0. 5 greater than the interquartile range for Marcus’s data.