Hannah's meteoric observations over the course of an hour.

To find how the mean and standard deviation are affected, we first need to calculate the original mean and standard deviation of Hannah's meteor counts. Original data: [6, 4, 10, 3, 7] Mean: (6 + 4 + 10 + 3 + 7) / 5 = 30 / 5 = 6 Standard deviation: Step 1: Calculate the deviations from the mean: [-0, -2, 4, -3, 1] Step 2: Square the deviations: [0, 4, 16, 9, 1] Step 3: Calculate the mean of the squared deviations: (0 + 4 + 16 + 9 + 1) / 5 = 30 / 5 = 6 Step 4: Take the square root of the mean of squared deviations: √6 ≈ 2.45 Now, let's see how adding 10 meteors in the next minute affects the data. Updated data: [6, 4, 10, 3, 7, 10] New mean: (6 + 4 + 10 + 3 + 7 + 10) / 6 = 40 / 6 ≈ 6.67 New standard deviation: Step 1: Calculate the deviations from the new mean: [-0.67, -2.67, 3.33, -3.67, 0.33, 3.33] Step 2: Square the deviations: [0.4489, 7.1289, 11.0889, 13.4689, 0.1089, 11.0889] Step 3: Calculate the mean of the squared deviations: (0.4489 + 7.1289 + 11.0889 + 13.4689 + 0.1089 + 11.0889) / 6 ≈ 7.2223 Step 4: Take the square root of the mean of squared deviations: √7.2223 ≈ 2.69 With the new datapoint, the mean increased from 6 to about 6.67, and the standard deviation increased from about 2.45 to 2.69. This means, on average, Hannah saw more meteors per minute, and there was a slight increase in the spread of meteors seen per minute.