Outliers from cumulative frequency diagram

6 The birth weights in grams of a random sample of 1000 babies are displayed in the cumulative frequency diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{05b96db3-93c7-4921-a1c6-c7b2f8952a8f-4_1264_1553_486_296}

1. Use the diagram to estimate the median and interquartile range of the data.
2. Use your answers to part (i) to estimate the number of outliers in the sample.
3. Should these outliers be excluded from any further analysis? Briefly explain your answer.
4. Any baby whose weight is below the 10th percentile is selected for careful monitoring. Use the diagram to determine the range of weights of the babies who are selected.
   \(12 \%\) of new-born babies require some form of special care. A maternity unit has 17 new-born babies. You may assume that these 17 babies form an independent random sample.
5. Find the probability that
   (A) exactly 2 of these 17 babies require special care,
   (B) more than 2 of the 17 babies require special care.
6. On 100 independent occasions the unit has 17 babies. Find the expected number of occasions on which there would be more than 2 babies who require special care.

3 The birth weights of 200 lambs from crossbred sheep are illustrated by the cumulative frequency diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{ab4d5ab1-e3b7-495f-9142-d37df7e712de-3_919_1144_430_476}

1. Estimate the percentage of lambs with birth weight over 6 kg .
2. Estimate the median and interquartile range of the data.
3. Use your answers to part (ii) to show that there are very few, if any, outliers. Comment briefly on whether any outliers should be disregarded in analysing these data. The box and whisker plot shows the birth weights of 100 lambs from Welsh Mountain sheep.
   \includegraphics[max width=\textwidth, alt={}, center]{ab4d5ab1-e3b7-495f-9142-d37df7e712de-3_321_1610_1818_293}
4. Use appropriate measures to compare briefly the central tendencies and variations of the weights of the two types of lamb.
5. The weight of the largest Welsh Mountain lamb was originally recorded as 6.5 kg , but then corrected. If this error had not been corrected, how would this have affected your answers to part (iv)? Briefly explain your answer.
6. One lamb of each type is selected at random. Estimate the probability that the birth weight of both lambs is at least 3.9 kg .

1 The birth weights in grams of a random sample of 1000 babies are displayed in the cumulative frequency diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{088972e9-bfcd-429c-9145-af274a4c0a58-1_1268_1548_472_335}

1. Use the diagram to estimate the median and interquartile range of the data.
2. Use your answers to part (i) to estimate the number of outliers in the sample.
3. Should these outliers be excluded from any further analysis? Briefly explain your answer.
4. Any baby whose weight is below the 10th percentile is selected for careful monitoring. Use the diagram to determine the range of weights of the babies who are selected.
   \(12 \%\) of new-born babies require some form of special care. A maternity unit has 17 new-born babies. You may assume that these 17 babies form an independent random sample.
5. Find the probability that
   (A) exactly 2 of these 17 babies require special care,
   (B) more than 2 of the 17 babies require special care.
6. On 100 independent occasions the unit has 17 babies. Find the expected number of occasions on which there would be more than 2 babies who require special care.

3 The birth weights in grams of a random sample of 1000 babies are displayed in the cumulative frequency diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{dfb0acd8-d84b-4291-a811-a68f4942794b-2_1266_1546_487_335}

1. Use the diagram to estimate the median and interquartile range of the data.
2. Use your answers to part (i) to estimate the number of outliers in the sample.
3. Should these outliers be excluded from any further analysis? Briefly explain your answer.
4. Any baby whose weight is below the 10th percentile is selected for careful monitoring. Use the diagram to determine the range of weights of the babies who are selected.
   \(12 \%\) of new-born babies require some form of special care. A maternity unit has 17 new-born babies. You may assume that these 17 babies form an independent random sample.
5. Find the probability that
   (A) exactly 2 of these 17 babies require special care,
   (B) more than 2 of the 17 babies require special care.
6. On 100 independent occasions the unit has 17 babies. Find the expected number of occasions on which there would be more than 2 babies who require special care.

3 The birth weights in grams of a random sample of 1000 babies are displayed in the cumulative frequency diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{79f1015b-7c3d-4576-8d5b-e9fc89d8a49e-2_1266_1546_487_335}

1. Use the diagram to estimate the median and interquartile range of the data.
2. Use your answers to part (i) to estimate the number of outliers in the sample.
3. Should these outliers be excluded from any further analysis? Briefly explain your answer.
4. Any baby whose weight is below the 10th percentile is selected for careful monitoring. Use the diagram to determine the range of weights of the babies who are selected.
   \(12 \%\) of new-born babies require some form of special care. A maternity unit has 17 new-born babies. You may assume that these 17 babies form an independent random sample.
5. Find the probability that
   (A) exactly 2 of these 17 babies require special care,
   (B) more than 2 of the 17 babies require special care.
6. On 100 independent occasions the unit has 17 babies. Find the expected number of occasions on which there would be more than 2 babies who require special care.

7 The birth weights of 200 lambs from crossbred sheep are illustrated by the cumulative frequency diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{4b259fe3-73ef-419f-85ad-1a3b1e6ea56e-4_917_1146_367_447}

1. Estimate the percentage of lambs with birth weight over 6 kg .
2. Estimate the median and interquartile range of the data.
3. Use your answers to part (ii) to show that there are very few, if any, outliers. Comment briefly on whether any outliers should be disregarded in analysing these data. The box and whisker plot shows the birth weights of 100 lambs from Welsh Mountain sheep.
   \includegraphics[max width=\textwidth, alt={}, center]{4b259fe3-73ef-419f-85ad-1a3b1e6ea56e-4_328_1616_1749_260}
4. Use appropriate measures to compare briefly the central tendencies and variations of the weights of the two types of lamb.
5. The weight of the largest Welsh Mountain lamb was originally recorded as 6.5 kg , but then corrected. If this error had not been corrected, how would this have affected your answers to part (iv)? Briefly explain your answer.
6. One lamb of each type is selected at random. Estimate the probability that the birth weight of both lambs is at least 3.9 kg .

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.
\includegraphics[max width=\textwidth, alt={}, center]{252d5094-6cdd-4379-bcd5-ca6a5cc48c7a-3_956_1497_1361_269}
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: 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.