2. The temperature of a supermarket fridge is regularly checked to ensure that it is working correctly. Over a period of three months the temperature (measured in degrees Celsius) is checked 600 times. These temperatures are displayed in the cumulative frequency diagram below.
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i. Use the diagram to estimate the median and interquartile range of the data.
ii. Use your answers to part (i) to show that there are very few, if any, outliers in the sample.
Below is the frequency table for these data:
| Temperature | | \(( t\) degrees Celsius \()\) |
| \(3.0 \leq t \leq 3.4\) | \(3.4 < t \leq 3.8\) | \(3.8 < t \leq 4.2\) | \(4.2 < t \leq 4.6\) | \(4.6 < t \leq 5.0\) |
| Frequency | 25 | 125 | 243 | 157 | 50 |
iii. Use the table to calculate estimates for the mean and standard deviation.
iv. The temperatures are converted from degrees Celsius to degrees Fahrenheit using the formula \(F = 1.8 C + 32\). Hence estimate the mean and standard deviation of the temperatures in degrees Fahrenheit.