Question

Here is a sample data set.

346.6	346.8	370.6	378.6	401.3	402.4
403.9	416.8	417.6	431.9	433.7	454.3
460.9	460.9	460.9	481.8	481.9	483.4
484.4	485.3	485.7	486.3	488.3	490.2
490.7	493.3	496.3	496.3	496.6	501.8
506	518.5	548.1	548.4	548.8	552.6
565.8	570.9	572.5	575.2	575.2	575.2
609.6	629.1	633.1	652.9	673.5	681.8
706	714.1	740.8	743.6	755.7	758.1

24681012141618length (cm)300350400450500550600650700750800Frequency

Find the first quartile for this data set.
Q₁ =

Find the third quartile for this data set.
Q₃ =

Find the interquartile range for this data set.
IQR =

Find the lower value or limit separating the outliers from the nonoutliers. This value might not actually be in the table
Lower value =

Find the upper value or limit separating the outliers from the nonoutliers. This value might not actually be in the table.
Upper value =

[X] Enlarged Graph 18 16 14 12 10 8 6 Frequency 2 400 450 500 550 600 650 700 750 800 360 350 length (cm)

Answer 1

1)

The first quartile (or lower quartile or 25th percentile) is the median of the upper half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the upper half.

346.6   346.8   370.6   378.6   401.3   402.4   403.9   416.8   417.6   431.9   433.7   454.3   460.9   460.9   460.9   481.8   481.9   483.4   484.4   485.3   485.7   486.3   488.3   490.2   490.7   493.3   496.3   496.3   496.6   501.8   506   518.5   548.1   548.4   548.8   552.6   565.8   570.9   572.5   575.2   575.2   575.2   609.6   629.1   633.1   652.9   673.5   681.8   706   714.1   740.8   743.6   755.7   758.1   

So, the upper half is

346.6   346.8   370.6   378.6   401.3   402.4   403.9   416.8   417.6   431.9   433.7   454.3   460.9   460.9   460.9   481.8   481.9   483.4   484.4   485.3   485.7   486.3   488.3   490.2   490.7   493.3   496.3   

The median of these numbers is 460.9.

The first quartile (Q1) of the data set is 460.9.

2)

The third quartile (or lower quartile or 25th percentile) is the median of the botton half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the bottom half.

346.6   346.8   370.6   378.6   401.3   402.4   403.9   416.8   417.6   431.9   433.7   454.3   460.9   460.9   460.9   481.8   481.9   483.4   484.4   485.3   485.7   486.3   488.3   490.2   490.7   493.3   496.3   496.3   496.6   501.8   506   518.5   548.1   548.4   548.8   552.6   565.8   570.9   572.5   575.2   575.2   575.2   609.6   629.1   633.1   652.9   673.5   681.8   706   714.1   740.8   743.6   755.7   758.1   

So, the bottom half is

496.3   496.6   501.8   506   518.5   548.1   548.4   548.8   552.6   565.8   570.9   572.5   575.2   575.2   575.2   609.6   629.1   633.1   652.9   673.5   681.8   706   714.1   740.8   743.6   755.7   758.1   

The median of these numbers is 575.2.

The third quartile (Q3) of the data set is 575.2.

3)

The interquartile range is the difference between the third and first quartiles.

The third quartile is 575.2.

The first quartile is 460.9.

The interquartile range = 575.2 - 460.9 = 114.3.

4)

Lower Outlier Boundary = Q1 - 1.5 x IQR = 460.9 - 1.5 x 114.3 = 289.45

5)

Upper Outlier Boundary = Q3 + 1.5 x IQR = 575.2 + 1.5  x 114.3 = 746.65