13 i Compare the following two series of figures in respect of their dispersion by quartile measures Weight kgs 58 56 62 61 63 64 65 59 62 65 55 Height cm 117 112 127 123 125 130 106 119 121 132 108... - CODE PELAJAR

Question

13. (i) Compare the following two series of figures in respect of their dispersion by quartile measures :- Weight (kgs.) : 58 56 62 61 63 64 65 59 62 65 55 Height (cm.) : 117 112 127 123 125 130 106 119 121 132 108

Asked Nov 20 at 03:53

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Basic Answer

Step 1: Arrange the Data in Ascending Order

First, we need to arrange the data for both weight and height in ascending order.

Weight (kgs.):
55, 56, 58, 59, 61, 62, 62, 63, 64, 65, 65

Height (cm.):
106, 108, 112, 117, 119, 121, 123, 125, 127, 130, 132

Step 2: Calculate the Quartiles

Quartiles divide the data into four equal parts. We need to find Q1 (first quartile), Q2 (median), and Q3 (third quartile).

Weight (kgs.):

• Q1 (25th percentile): Position is (11 + 1) / 4 = 3 → 58 kg
• Q2 (50th percentile): Position is (11 + 1) / 2 = 6 → 62 kg
• Q3 (75th percentile): Position is 3 * (11 + 1) / 4 = 9 → 64 kg

Height (cm.):

• Q1 (25th percentile): Position is (11 + 1) / 4 = 3 → 112 cm
• Q2 (50th percentile): Position is (11 + 1) / 2 = 6 → 121 cm
• Q3 (75th percentile): Position is 3 * (11 + 1) / 4 = 9 → 127 cm

Step 3: Calculate the Interquartile Range (IQR)

The IQR is the difference between Q3 and Q1.

Weight (kgs.):
IQR = Q3 – Q1 = 64 – 58 = 6 kg

Height (cm.):
IQR = Q3 – Q1 = 127 – 112 = 15 cm

Step 4: Compare the Dispersion

The IQR gives us a measure of the spread of the middle 50% of the data.

• Weight (kgs.): IQR = 6 kg
• Height (cm.): IQR = 15 cm

Since the IQR for height (15 cm) is greater than the IQR for weight (6 kg), the height data has a greater dispersion compared to the weight data.

Final Answer

The height data has a greater dispersion compared to the weight data, as indicated by the larger Interquartile Range (IQR) of 15 cm for height versus 6 kg for weight.