Question

1. - / 2 points consider a sample with data values of 10, 20, 21, 14, 18 and 19. compute the mean and median. mean median 4. - / 3 points consider a sample with data values of 52, 54, 70, 59, 63, 57, 52, 69, 57, 67, and 52. compute the mean. (round your answer to two decimal places.) compute the median. compute the mode.

Explanation:

Problem 3:

Step1: Calculate the mean

The mean is the sum of all values divided by the number of values. The data values are 10, 20, 21, 14, 18, 19. The sum is \(10 + 20 + 21 + 14 + 18 + 19\). Let's compute that: \(10+20 = 30\), \(30+21 = 51\), \(51+14 = 65\), \(65+18 = 83\), \(83+19 = 102\). There are 6 values. So the mean is \(\frac{102}{6}\).
\( \frac{102}{6} = 17 \)

Step2: Calculate the median

First, we need to sort the data in ascending order: 10, 14, 18, 19, 20, 21. Since there are 6 values (an even number), the median is the average of the two middle values. The two middle values are the 3rd and 4th values, which are 18 and 19. So the median is \(\frac{18 + 19}{2}\).
\( \frac{18 + 19}{2} = \frac{37}{2} = 18.5 \)

Step1: Calculate the mean

The data values are 52, 54, 70, 59, 63, 57, 52, 69, 57, 67, 52. First, find the sum. Let's add them up:
52 + 54 = 106; 106 + 70 = 176; 176 + 59 = 235; 235 + 63 = 298; 298 + 57 = 355; 355 + 52 = 407; 407 + 69 = 476; 476 + 57 = 533; 533 + 67 = 600; 600 + 52 = 652.
There are 11 values. So the mean is \(\frac{652}{11}\) (rounded to two decimal places).
\( \frac{652}{11} \approx 59.27 \)

Step2: Calculate the median

Sort the data in ascending order: 52, 52, 52, 54, 57, 57, 59, 63, 67, 69, 70. There are 11 values, so the median is the 6th value (since \((11 + 1)/2 = 6\)). The 6th value is 57.

Step3: Calculate the mode

The mode is the value that appears most frequently. Looking at the sorted data, 52 appears 3 times, which is more than any other value (57 appears 2 times, others appear once). So the mode is 52.

Answer:

mean: \(17\)
median: \(18.5\)

Problem 4: