Question

b) {52, 56, 61, 63, 64, 64, 71, 75, 79, 79, 79, 81, 87, 88, 90, 95} 16
q₁: 63.5 étendue du 1ᵉ quart: 63.5 - 52 = 11.5 médiane: 77
q₃:
éi:
e:
mode:
moyenne: (52 + 56+61+63 + 64+64 + 71 + 75+79+79+79 + 81+87 + 88+90+95)/16

Explanation:

Step1: Find the third - quartile ($Q_3$)

The data set has $n = 16$ values. First, order the data. The position of $Q_3$ is at $0.75\times(n + 1)=0.75\times(16 + 1)=12.75$. The 12th value is 87 and the 13th value is 88. So $Q_3=\frac{87 + 88}{2}=87.5$.

Step2: Calculate the inter - quartile range ($IQR$ or $ÉI$)

$IQR=Q_3 - Q_1$. Given $Q_1 = 63.5$, then $IQR=87.5-63.5 = 24$.

Step3: Calculate the range ($E$)

The range is the difference between the maximum and minimum values. The maximum value is 95 and the minimum value is 52. So $E=95 - 52=43$.

Step4: Find the mode

The mode is the most frequently occurring value. In the data set, 79 occurs 3 times, more frequently than any other value. So the mode is 79.

Step5: Calculate the mean (Moyenne)

The sum of the data values is $52+56 + 61+63+64+64+71+75+79+79+79+81+87+88+90+95=1164$. The mean $\bar{x}=\frac{1164}{16}=72.75$.

Answer:

$Q_3:87.5$
$ÉI:24$
$E:43$
Mode:79
Moyenne:72.75