Question

1. find the mean, mode, median, and midrange for the following data set. 12, 15, 18, 18, 15, 22, 15, 30, 12 a) mean = 21.0 mode = 15 median = 15 midrange = 17.4 b) mean = 15 mode = 15 median = 17.4 midrange = 21.0 c) mean = 17.4 mode = 15 median = 15 midrange = 21.0 d) mean = 17.4 mode = 18 median = 15 midrange = 21.0

Explanation:

Step1: Organize the data

First, sort the data set: \(12, 12, 15, 15, 15, 18, 18, 22, 30\) (wait, original data is \(12, 15, 18, 18, 15, 22, 15, 30, 12\)? Wait, let's count the numbers. Let's list them: 12, 15, 18, 18, 15, 22, 15, 30, 12. So that's 9 numbers. Sorting: 12, 12, 15, 15, 15, 18, 18, 22, 30.

Step2: Calculate the mean

Mean is sum of data divided by number of data points. Sum: \(12 + 12 + 15 + 15 + 15 + 18 + 18 + 22 + 30\). Let's calculate: \(12+12=24\); \(15+15+15=45\); \(18+18=36\); \(22+30=52\). Total sum: \(24 + 45 + 36 + 52 = 24+45=69; 69+36=105; 105+52=157\)? Wait, no, wait: 12,12,15,15,15,18,18,22,30. Let's add again: 12+12=24; 153=45; 182=36; 22+30=52. So 24+45=69; 69+36=105; 105+52=157? Wait, but 9 data points. Wait, maybe I miscounted. Wait original data: 12,15,18,18,15,22,15,30,12. Let's count: 12 (1), 15 (2), 18 (3), 18 (4), 15 (5), 22 (6), 15 (7), 30 (8), 12 (9). Yes, 9. So sum: 12+15=27; +18=45; +18=63; +15=78; +22=100; +15=115; +30=145; +12=157. So mean is \(157 / 9 \approx 17.444...\) so approximately 17.4.

Step3: Find the mode

Mode is the most frequent number. 15 appears 3 times (positions 2,5,7), 12 appears 2 times, 18 appears 2 times, 22 and 30 once. So mode is 15.

Step4: Find the median

Median is the middle value (since 9 data points, the 5th term). Sorted data: 12,12,15,15,15,18,18,22,30. The 5th term is 15.

Step5: Calculate midrange

Midrange is \(\frac{\text{maximum} + \text{minimum}}{2}\). Maximum is 30, minimum is 12. So \(\frac{30 + 12}{2} = \frac{42}{2} = 21.0\).

Now let's check the options:

Option C: mean=17.4, mode=15, median=15, midrange=21.0. Which matches our calculations.

Answer:

C) mean = 17.4, mode = 15, median = 15, midrange = 21.0