Question

a chemistry teacher asked his class to record their heart rates while sitting. here is the class data.
68 80 61 76 66 100 55 74 64 73 70 68 78 47 62.
(a)
find the mean of the data to the one - hundredth place.
a 69.83
b 68.67
c 70.19
d 69.47
(b)
find the interquartile range.
a 12
b 14

Explanation:

Step1: Calculate the sum of data

Sum \( S=68 + 80+61 + 76+66 + 100+55 + 74+64 + 73+70 + 68+78 + 47+62\)
\(S = 1047\)

Step2: Calculate the number of data points

Number of data points \(n = 15\)

Step3: Calculate the mean

Mean \(\bar{x}=\frac{S}{n}=\frac{1047}{15}=69.8\) (exact value). Rounding to two - decimal places: \(\bar{x}\approx69.83\)

Step4: Sort the data

Sort the data: \(47,55,61,62,64,66,68,68,70,73,74,76,78,80,100\)

Step5: Find the median (Q2)

Since \(n = 15\), the median (Q2) is the 8th value. So \(Q2 = 68\)

Step6: Find Q1

The lower half of the data is \(47,55,61,62,64,66,68\). The median of the lower half (Q1) is the 4th value. So \(Q1=62\)

Step7: Find Q3

The upper half of the data is \(70,73,74,76,78,80,100\). The median of the upper half (Q3) is the 4th value. So \(Q3 = 76\)

Step8: Calculate the inter - quartile range (IQR)

\(IQR=Q3 - Q1=76 - 62 = 14\)

Answer:

a) A. 69.83
b) B. 14