Question

Lily measured the lengths of 16 fish.

Use the graph below to estimate the lower and upper quartiles of the fish

Answer 1

The lower quartile of the fish lengths is estimated to be 2, while the upper quartile is estimated to be 9.

Step-by-step explanation:

The lower quartile (Q1) of the fish lengths can be estimated as the median of the lower half of the data. Since there are 16 measurements, divide the data into two halves with 8 measurements each. The lower quartile will be the value in the middle of the lower half, which is the 4th value. Counting from the smallest value, the 4th value is 2.

The upper quartile (Q3) can be estimated as the median of the upper half of the data. Using the same procedure, the upper quartile will be the value in the middle of the upper half, which is the 12th value. Counting from the smallest value, the 12th value is 9.

Answer 2

The lower quartile of the fish lengths is 15 inches

The upper quartile of the fish lengths is 30 inches

Step-by-step explanation:

(the cumulative frequency gives how much of the observations/measurements are under a certain value e.g, in our case, for lengths of 40 inches, all 16 of the fish have length in that range (less than or equal to 40) so, the cumulative frequency is 16 and so on)

We need to find the lower and upper quartiles of the fish lengths,

Now, the lower quartile contains 25% (or 1/4) of the values

in our case, since there are 16 fish,

25% of 16 is 4

So, for the lower quartile, the cumulative frequency should be 4.

For which the length is 15 inches,

So, the lower quartile of the fish lengths is 15 inches

The upper quartile contains 75% (or 3/4) of the values,

Now, 3/4 of 16 is 12.

So, for the upper quartile, the cumulative frequency should be 12.

For which the length is 30 inches

So, the upper quartile of the fish lengths is 30 inches