Question

Determine the minimum, maximum, and quartile values. Remember, the first step is to put the values in order from least to greatest.

{109,107,109,105,102,103,110,101,104,105,105}

Answer 1

The minimum value for the data set is 101, the maximum value is 110, the first quartile (Q1) is 103, the median (Q2) is 105, the third quartile (Q3) is 109, and the Interquartile Range (IQR) is 6.

Step-by-step explanation:

Calculating Minimum, Maximum, and Quartiles

To determine the minimum, maximum, and quartile values for a data set, we must first organize the data in ascending order. Let's arrange the given data set: {101, 102, 103, 104, 105, 105, 105, 107, 109, 109, 110}.

Minimum value (smallest): 101

Maximum value (largest): 110

Next, we find the quartiles:

Median (Q2 or second quartile): This is the middle value of the data set. Since there are 11 values, the sixth value is the median, which is 105.

First quartile (Q1): This is the median of the lower half of the data set (excluding the median if there is an odd number of data points). In this case, the lower half is {101, 102, 103, 104, 105}, so the median is 103.

Third quartile (Q3): This is the median of the upper half of the data set (excluding the median if there is an odd number of data points). The upper half is {105, 107, 109, 109, 110}, so the median is 109.

Finally, to calculate the Interquartile Range (IQR), you subtract Q1 from Q3: IQR = Q3 - Q1 = 109 - 103 = 6.