Question

At a high school track meet, there are two heats, or races, for the 100-meter hurdles event. The results, in seconds, of each heat are shown in the table to the right.

Predict which of the heats has the smaller standard deviation and use your dot plot to justify your answer.
Find the mean and the standard deviation for each of the heats. Record your answer below.

Answer 1

To predict which of the heats has the smaller standard deviation in a high school track meet, we need to calculate the mean and standard deviation for each heat. By comparing the standard deviations, we can determine that Heat 2 has the smaller standard deviation.

Step-by-step explanation:

The question asks us to predict which of the heats in a high school track meet has the smaller standard deviation. To find this, we need to calculate the mean and standard deviation for each heat. Let's start with Heat 1:

Mean = (10.8 + 11.2 + 11.4 + 11.5 + 11.7)/5 = 56.6/5 = 11.32 seconds

Standard Deviation = sqrt((10.8-11.32)^2 + (11.2-11.32)^2 + (11.4-11.32)^2 + (11.5-11.32)^2 + (11.7-11.32)^2)/5 = sqrt(0.0272 + 0.0432 + 0.0144 + 0.0048 + 0.0624)/5 = sqrt(0.152)/5 ≈ 0.13873 seconds

Now let's move on to Heat 2:

Mean = (11.1 + 11.2 + 11.3 + 11.5 + 11.5)/5 = 56.6/5 = 11.32 seconds

Standard Deviation = sqrt((11.1-11.32)^2 + (11.2-11.32)^2 + (11.3-11.32)^2 + (11.5-11.32)^2 + (11.5-11.32)^2)/5 = sqrt(0.0488 + 0.0144 + 0.0008 + 0.0048 + 0.0048)/5 = sqrt(0.0736)/5 ≈ 0.08581 seconds

Comparing the standard deviations, we can see that Heat 2 has the smaller standard deviation of approximately 0.08581 seconds, which is smaller than the standard deviation of Heat 1 of approximately 0.13873 seconds. This means that the times in Heat 2 are more consistent and closer to the mean compared to the times in Heat 1.

Keywords: heat, standard deviation, mean, track meet, dot plot

Answer 2

Standard deviation is a measure of dispersion in a set of values. Without the actual times for the heats, the specific standard deviation cannot be calculated. However, the concept and calculation method can still be explained in general terms.

Step-by-step explanation:

The student is tasked with predicting which of two heats for the 100-meter hurdles event at a high school track meet has the smaller standard deviation and finding the mean and standard deviation for each of the heats. Unfortunately, the data for the heats is not provided, so it is not possible to calculate the exact standard deviation without this information. However, we can discuss the concept of standard deviation in general terms.

The standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values. To arrive at the standard deviation, one would typically follow these steps:

1. Calculate the mean of the data set.
2. Subtract the mean from each data point and square the result.
3. Calculate the mean of these squared differences.
4. Take the square root of the mean squared differences. This gives the standard deviation.

For example, if one of the heats has times that are very close to each other while the other heat has times that are more spread out, the heat with the more clustered times would have a smaller standard deviation.

As for the provided information on various individuals and their mile running times, we can note the relationship between individual times and the class mean and standard deviation. For instance, if Rachel ran the mile in eight minutes while her class's mean is 11 minutes with a standard deviation of three minutes, her time is one standard deviation below the mean, which is relatively faster than average for her class.