Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 19: Review in context

Dr Roussianos asked cardiology patients to measure their systolic blood pressure each Saturday morning for ten weeks.

Here is the data for three patients.

Patient $1$

Patient $2$

Patient $3$

This table shows the treatments recommended for different values of the yearly mean and standard deviation.

Calculate the mean and use the sample data to estimate the yearly statistics and therefore help to determine the treatment for each patient.

$80$ people were asked to measure their pulse rate as soon as they woke up in the morning.

The summary statistics are: $\sum _{}x=6000$ and $\sum _{}{x}^2=452450$.

From this information, find the mean and the standard deviation of the data set. If this was a sample of the population, state the inferences which could be drawn from this sample data set.

Birth mass follows a normal distribution. The summary statistics for the masses of $50$ babies in a hospital were $\sum _{}x=160 \mathrm{kg}$ and $\sum _{}{x}^2=524$.

Calculate the mean baby mass and the standard deviation of the sample.

Birth mass follows a normal distribution. The summary statistics for the masses of $50$ babies in a hospital were $\sum _{}x=160 \mathrm{kg}$ and $\sum _{}{x}^2=524$.

If a baby's mass is less than $2.5$ times the standard deviation below the mean, the baby is at risk. Find a value of $x$, so that babies who weigh less than $x$ kg are considered to be at risk.

In one town, $300$ mothers were asked their age at the birth of their first child. The results are given in the table.

Estimate the mean and standard deviation for a mother's age at the birth of her first child for this town.

The summary statistics for $30$ years ago, for a different sample of $300$ women were $\sum _{}x=7500$ and $\sum _{}{x}^2=190000$. State the infereces that can be drawn from the data.