The stem-and-leaf plot represents the average monthly high temperatures in Tampa, Florida. What is the first quartile (Q1) of the temperatures? Round to the nearest tenth.
Stem leaf
6 9
7 1267
8 14799
9 00
To find the first quartile (Q1) of the temperatures represented in the stem-and-leaf plot, you need to understand the concept of quartiles. A quartile divides a set of data into four equal parts. Q1 represents the value below which 25% of the data lies.
To find Q1, you can follow these steps:
1. Arrange the data in ascending order: 0, 0, 1, 2, 2, 7, 9, 9, 9.
2. Calculate the position of Q1 using the formula: position = (n + 1) / 4, where n is the total number of data points. In this case, n = 9 (the total number of data points), so the position = (9+1)/4 = 10/4 = 2.5.
3. Since the position is not a whole number, you need to interpolate. Interpolation means finding the value between two existing data points. In this case, the value between the second and third data points (1 and 2) would be interpolated.
4. The interpolated value can be calculated using the formula: interpolated value = L + (P - L) * f, where L is the lower value, P is the position, and f is the fractional part. In this case, L = 1, P = 2.5, and f = 0.5.
- interpolated value = 1 + (2.5 - 1) * 0.5 = 1 + 1.5 * 0.5 = 1 + 0.75 = 1.75.
5. So, the first quartile Q1 is approximately 1.8 (rounded to the nearest tenth) based on the stem-and-leaf plot of the average monthly high temperatures in Tampa, Florida.